MATH 200 UCI Standardized Z Score Averages Proportions & Variables Worksheet

Question Description

Show ALL work and use appropriate notation. If using a calculator, state the programs

and/or commands you are using. Round ALL answers to three decimal places, unless

otherwise specified.

1. Julie’s height, when compared to other females her age, has a standardized z-score of 0.28.

a. Is Julie taller or shorter than the average female her age? Explain.

b. What proportion of females her age is Julie taller than?

2. Braden is taking a multiple choice exam in a language he doesn’t read or speak. There are 18

questions and each question has choices A, B, C, and D to choose from. Braden’s only option

is to guess. Let X represent the number of correct guesses.

a. Does X represent a discrete or continuous variable? How many values are possible

for X.

b. Find the probability Braden guesses correctly on the seventh question.

c. Find the probability Braden guesses correctly on exactly half of the questions.

3. The weekly salary of teachers in one state is normally distributed with a mean of $870 and a

standard deviation of $85.

a. What is the probability that a randomly selected teacher earns between $800 and $900

per week?

b. What is the weekly salary that determines the top earning 2% of teachers? Round

your answer to the nearest cent.

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